Primitive solutions of the Kortewegde Vries equation
Abstract
We survey recent results connected with constructing a new family of solutions of the Kortewegde Vries equation, which we call primitive solutions. These solutions are constructed as limits of rapidly vanishing solutions of the Kortewegde Vries equation as the number of solitons tends to infinity. A primitive solution is determined nonuniquely by a pair of positive functions on an interval on the imaginary axis and a function on the real axis determining the reflection coefficient. We show that elliptic onegap solutions and, more generally, periodic finitegap solutions are special cases of reflectionless primitive solutions.
 Publication:

Theoretical and Mathematical Physics
 Pub Date:
 April 2020
 DOI:
 10.1134/S0040577920030058
 Bibcode:
 2020TMP...202..334D
 Keywords:

 integrable system;
 Kortewegde Vries equation;
 primitive solution